The traditional multi-view feature extraction (MvFE) method usually seeks a latent common subspace where the samples from different views are maximally correlated. Recently, the regression-based method has become one of the most effective feature extraction methods. However, the existing regression-based methods are only suitable for single-view cases. In this paper, we firstly propose a new MvFE method named as cross-regression for MvFE (CRMvFE). CRMvFE designs a novel cross-regression regularization term to discover the relationship between multiple views in the original space, and simultaneously obtains the low-dimensional projection matrix for each view. Furthermore, inspired by the robustness of L2,1-norm, we also propose a robust CRMvFE (RCRMvFE) and an iterative algorithm to find the optimal solution. Theoretical analysis of the convergence and the relationship with CRMvFE demonstrate the effectiveness of the proposed RCRMvFE. Experiments on datasets show that the proposed CRMvFE and RCRMvFE have better performance than other related methods.

传统的多视图特征提取（MvFE）方法通常会寻找潜在的公共子空间，在该子空间中，来自不同视图的样本具有最大的相关性。近年来，基于回归的方法已成为最有效的特征提取方法之一。但是，现有的基于回归的方法仅适用于单视图情况。在本文中，我们首先提出了一种新的MvFE方法，称为MvFE交叉回归（CRMvFE）。CRMvFE设计了一种新颖的交叉回归正则化项，以发现原始空间中多个视图之间的关系，并同时获取每个视图的低维投影矩阵。此外，受L2,1-范数的鲁棒性启发，我们还提出了鲁棒的CRMvFE（RCRMvFE）和迭代算法以找到最佳解决方案。对收敛性及其与CRMvFE的关系的理论分析证明了所提出的RCRMvFE的有效性。在数据集上的实验表明，所提出的CRMvFE和RCRMvFE具有比其他相关方法更好的性能。